Find the value of sin²25° + sin²65° + coses²57° - tan²33° = ?

Solution(By Examveda Team)

$${\sin ^2}{25^ \circ } + {\sin ^2}{65^ \circ } + {\text{cose}}{{\text{c}}^2}{57^ \circ } - {\text{ta}}{{\text{n}}^2}{33^ \circ }$$
$$ \Rightarrow \left( {{{\sin }^2}{{25}^ \circ } + {{\cos }^2}{{25}^ \circ }} \right) + $$     $$\left( {{\text{se}}{{\text{c}}^2}{{33}^ \circ } - {\text{ta}}{{\text{n}}^2}{{33}^ \circ }} \right)$$
$$\eqalign{ & \Rightarrow 1 + 1 \cr & \Rightarrow 2 \cr & {\bf{Note:}} \cr & {\sin ^2}{65^ \circ } = {\sin ^2}\left( {{{90}^ \circ } - {{25}^ \circ }} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{co}}{{\text{s}}^2}{25^ \circ } \cr & {\text{cose}}{{\text{c}}^2}{57^ \circ } = {\operatorname{cosec} ^2}\left( {{{90}^ \circ } - {{33}^ \circ }} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{se}}{{\text{c}}^2}{33^ \circ } \cr} $$